TSTP Solution File: SWC063+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC063+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:22:58 EDT 2023
% Result : Theorem 11.29s 11.49s
% Output : Proof 11.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC063+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 16:43:55 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 11.29/11.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MMkfKXuYiD/cvc5---1.0.5_19969.p...
% 11.29/11.49 ------- get file name : TPTP file name is SWC063+1
% 11.29/11.49 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19969.smt2...
% 11.29/11.49 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.29/11.49 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.29/11.49 % SZS status Theorem for SWC063+1
% 11.29/11.49 % SZS output start Proof for SWC063+1
% 11.29/11.49 (
% 11.29/11.49 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssList Z)) (not (= (tptp.app _let_1 Z) W)) (not (= (tptp.app Z _let_1) X))))))) (tptp.neq X tptp.nil)) (and (or (not (= tptp.nil V)) (= tptp.nil U)) (or (not (tptp.neq V tptp.nil)) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (tptp.neq X1 tptp.nil) (tptp.segmentP V X1) (tptp.segmentP U X1)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_11 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_12 (tptp.app _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_14 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14))) (let ((_let_16 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (tptp.app _let_12 tptp.nil))) (let ((_let_18 (= _let_17 (tptp.app _let_11 _let_14)))) (let ((_let_19 (tptp.segmentP _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_13))) (let ((_let_23 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_22 _let_21))) (let ((_let_28 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_29 (and _let_27 _let_28))) (let ((_let_30 (not _let_27))) (let ((_let_31 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_32 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (not _let_32))) (let ((_let_34 (and _let_33 _let_31))) (let ((_let_35 (forall ((X1 $$unsorted)) (or (not (tptp.ssList X1)) (not (tptp.neq X1 tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X1)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X1)))))) (let ((_let_36 (not _let_35))) (let ((_let_37 (not _let_28))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (not _let_31))) (let ((_let_40 (or _let_39 _let_32))) (let ((_let_41 (and _let_40 _let_38))) (let ((_let_42 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_41 _let_34 _let_29))) (let ((_let_45 (forall ((U $$unsorted) (BOUND_VARIABLE_5438 $$unsorted) (BOUND_VARIABLE_5436 $$unsorted) (BOUND_VARIABLE_5434 $$unsorted)) (let ((_let_1 (tptp.neq BOUND_VARIABLE_5434 tptp.nil))) (let ((_let_2 (tptp.cons BOUND_VARIABLE_5438 tptp.nil))) (let ((_let_3 (= tptp.nil BOUND_VARIABLE_5434))) (let ((_let_4 (= tptp.nil U))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5434)) (and (or (not _let_3) _let_4) (or (not _let_1) (not (forall ((X1 $$unsorted)) (or (not (tptp.ssList X1)) (not (tptp.neq X1 tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5434 X1)) (not (tptp.segmentP U X1))))))) (and (not _let_4) _let_3) (and (or (not (tptp.ssItem BOUND_VARIABLE_5438)) (not (tptp.ssList BOUND_VARIABLE_5436)) (not (= U (tptp.app _let_2 BOUND_VARIABLE_5436))) (not (= BOUND_VARIABLE_5434 (tptp.app BOUND_VARIABLE_5436 _let_2)))) _let_1))))))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (or))) (let ((_let_49 (not _let_45))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_47) :args (_let_49))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_45))) (REFL :args (_let_46)) :args _let_48)) _let_47 :args (_let_46 true _let_45)))) (let ((_let_51 (tptp.neq tptp.nil tptp.nil))) (let ((_let_52 (REFL :args (_let_39)))) (let ((_let_53 (_let_34))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 2)) _let_50 :args ((not _let_41) true _let_44)))) (let ((_let_55 (CNF_AND_NEG :args (_let_41)))) (let ((_let_56 (REFL :args (_let_38)))) (let ((_let_57 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_28))) :args _let_48)) :args ((or _let_28 _let_38))))) (let ((_let_58 (not _let_51))) (let ((_let_59 (not _let_8))) (let ((_let_60 (or _let_59 _let_59 _let_58))) (let ((_let_61 (forall ((U $$unsorted) (BOUND_VARIABLE_3292 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3292)) (= (tptp.neq U BOUND_VARIABLE_3292) (not (= U BOUND_VARIABLE_3292))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 (ASSUME :args (_let_8)))) (let ((_let_65 (and _let_31 _let_58))) (let ((_let_66 (ASSUME :args (_let_58)))) (let ((_let_67 (APPLY_UF tptp.neq))) (let ((_let_68 (REFL :args (tptp.nil)))) (let ((_let_69 (ASSUME :args (_let_31)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST _let_55 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_31))) :args _let_48)) :args ((or _let_31 _let_40))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_65)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_69) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_69) _let_68 :args _let_67) (FALSE_INTRO _let_66))) :args (_let_58 _let_31))) :args (_let_31 _let_58))) :args (true _let_65)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_51))) (REFL :args (_let_37)) :args _let_48)) :args ((or _let_39 _let_37 _let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_60))) :args ((or _let_59 _let_58 (not _let_60)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63))) _let_62 :args (_let_60 false _let_61)) :args (_let_58 false _let_8 false _let_60)) _let_57 _let_55 _let_54 (CNF_OR_NEG :args (_let_40 1)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_53) (CONG (REFL :args _let_53) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) _let_52 :args _let_48)) :args ((or _let_39 _let_32 _let_34))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 3)) _let_50 :args ((not _let_34) true _let_44)) :args (_let_39 true _let_51 false _let_28 true _let_38 true _let_41 false _let_40 false _let_32 true _let_34)) :args (_let_40 true _let_31)) :args ((not _let_38) true _let_41 false _let_40)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST _let_57 _let_70 :args (_let_28 true _let_38)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_29)) :args ((or _let_37 _let_29 _let_30))) _let_71 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 4)) _let_50 :args ((not _let_29) true _let_44)) :args (_let_30 false _let_28 true _let_29)))) (let ((_let_73 (REFL :args (_let_27)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 2)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_13))) :args _let_48)) :args ((or _let_13 _let_27))) _let_72 :args (_let_13 true _let_27)))) (let ((_let_75 (or _let_24 _let_15))) (let ((_let_76 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_ENUM))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_48)) :args ((or _let_23 _let_27))) _let_72 :args (_let_23 true _let_27)))) (let ((_let_80 (not _let_16))) (let ((_let_81 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_24 _let_84 _let_82 _let_80))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_48)) :args ((or _let_35 _let_38))) _let_70 :args (_let_35 true _let_38)))) (let ((_let_87 (_let_35))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_90 (tptp.segmentP (tptp.app _let_89 _let_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_91 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_89))) (let ((_let_92 (tptp.ssList _let_11))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_24 _let_24 _let_95 _let_59 _let_93 _let_90))) (let ((_let_97 (forall ((U $$unsorted) (BOUND_VARIABLE_4466 $$unsorted) (BOUND_VARIABLE_4464 $$unsorted) (BOUND_VARIABLE_4462 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4462)) (not (tptp.segmentP U BOUND_VARIABLE_4462)) (not (tptp.ssList BOUND_VARIABLE_4466)) (not (tptp.ssList BOUND_VARIABLE_4464)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4466 U) BOUND_VARIABLE_4464) BOUND_VARIABLE_4462))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (_let_97))) (let ((_let_100 (or _let_24 _let_94))) (let ((_let_101 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_101))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_24 _let_94 (not _let_100)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args _let_78) :args _let_103)) _let_102 :args (_let_100 false _let_101)) :args (_let_94 false _let_23 false _let_100)))) (let ((_let_105 (or _let_59 _let_26 _let_92))) (let ((_let_106 (forall ((U $$unsorted) (BOUND_VARIABLE_3315 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3315)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3315 U)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_48)) :args ((or _let_25 _let_27))) _let_72 :args (_let_25 true _let_27)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_59 _let_26 _let_92 (not _let_105)))) _let_64 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM)) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_92 false _let_8 false _let_25 false _let_105)))) (let ((_let_110 (or _let_24 _let_91))) (let ((_let_111 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (_let_111))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 3)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_48)) :args ((or _let_20 _let_27))) _let_72 :args (_let_20 true _let_27)))) (let ((_let_115 (and _let_20 _let_91 _let_90))) (let ((_let_116 (ASSUME :args (_let_90)))) (let ((_let_117 (APPLY_UF tptp.segmentP))) (let ((_let_118 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_119 (APPLY_UF tptp.app))) (let ((_let_120 (REFL :args (_let_11)))) (let ((_let_121 (ASSUME :args (_let_91)))) (let ((_let_122 (ASSUME :args (_let_20)))) (let ((_let_123 (SYMM _let_122))) (let ((_let_124 (SYMM _let_123))) (let ((_let_125 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_126 (not _let_125))) (let ((_let_127 (= _let_126 _let_83))) (let ((_let_128 (or _let_24 _let_59 _let_127))) (let ((_let_129 (= tptp.nil (tptp.app tptp.nil tptp.nil)))) (let ((_let_130 (= _let_11 (tptp.app _let_11 tptp.nil)))) (let ((_let_131 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_132 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_133 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_134 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_135 (not _let_132))) (let ((_let_136 (not _let_133))) (let ((_let_137 (not _let_134))) (let ((_let_138 (or _let_43 _let_137 _let_136 _let_135))) (let ((_let_139 (or _let_59 _let_129))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_59 _let_129 (not _let_139)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (tptp.nil QUANTIFIERS_INST_ENUM)) :args _let_113)) _let_112 :args (_let_139 false _let_111)) :args (_let_129 false _let_8 false _let_139)))) (let ((_let_141 (or _let_59 _let_26 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X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_10 _let_9 _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_6 _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_4 _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.29/11.50 )
% 11.29/11.50 % SZS output end Proof for SWC063+1
% 11.29/11.50 % cvc5---1.0.5 exiting
% 11.29/11.50 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------